Definition of Vertical Asymptotes

Vertical asymptotes are straight lines of the equation , toward which a function f(x) approaches infinitesimally closely, but never reaches the line, as f(x) increases without bound. For these values of x, the function is either unbounded or is undefined. For example, the function has a vertical asymptote at , because the function is undefined there. Vertical asymptotes occur when the limit of a function approaches ±∞, known as a singularity. A function can have any number of vertical asymptotes, such as the function , which has them every radians, where n is an integer. Vertical asymptotes can be determined using one-sided limits.